Question

If the width and height of a rectangular prism are each shrunk to one seventh of the original size but the length remains the same, what is the formula to find the modified surface area?

Answer 1

So the question ask to calculate the function or the formula that could be the solution if the width and height of a rectangular prism are shrunk to one seventh and the length stays the same, base on that, I would say that the surface area would be 2 ( 1/7w1/7h + l1/7w + l1/7h)

Answer 2

Answer:

The answer is $S_N=\frac{2}{7}*(L*H+L*W+\frac{W*H}{7})$

Step-by-step explanation:

In order to determine the formula, we have to know the expression of the volume of a rectangular prism.

I have attached an image that shows two formulas about the rectangular prism.

Therefore, using the same notation of the image:

L=length of the rectangular prism

W=width of the rectangular prism

H=height of the rectangular prism

So, the original surface area is:

$S_o=2*L*H+2*L*W+2*W*H$

Then, if the width and height of the rectangular prism are each shrunk to one seventh of the original size but the length remains the same, the new surface area is:

$S_N=2*L*\frac{H}{7}+2*L*\frac{W}{7}+2*\frac{W}{7}*\frac{H}{7}\\S_N=\frac{2}{7}*(L*H+L*W+\frac{W*H}{7})$

Finally, the formula of the modified surface area is $S_N$